Dispensing liquid from a non-vented rigid container (i.e., sufficiently rigid to resist collapsing when liquid is dispensed) requires that air be vented into the container through the valve to obtain proper flow. Use of a conventional, unvented valve for dispensing liquid will result in liquid flow, if any, that is uneven and insufficient in terms of flow-rate as air must enter the container through the liquid flow passage. Vented valves that allow air to flow into the container are known but have been found to be unsatisfactory for many applications. In some cases, these vented valves rely on use of a vent-tube that extends deep into the container, and these tubes are not suitable for certain applications and also increase cost and are unsightly when visible in the container. Known vented valves are overly complex and, thus, expensive due to material and assembly cost. Also, these known valves often include a seal element that is common to the vent passage and the liquid flow passage and, the simultaneous opening of these passages often results in poor results, especially when dispensing liquid from a pressurized container. In general, known vented valves have been deemed sub-optimal for a wide variety of reasons, and a need has been found for a new vented valve suitable for use in dispensing liquids from pressurized or non-pressurized rigid containers.